Living with Ambiguity: Pricing Mortality-Linked Securities with Smooth Ambiguity Preferences

Abstract

Mortality is a stochastic process. We have imprecise knowledge about the probability distribution of mortality rates in the future. Mortality risk, therefore, can be defined in a broad term of ambiguity. In this paper, we investigate the effects of ambiguity and ambiguity aversion on prices of mortality-linked securities. We adopt an asymmetric mortality jump model proposed by Chen et al. (2011) for mortality modeling and forecasting. Ambiguity may arise from parameter uncertainty due to a finite sample of data and inaccurate old-age mortality rates. We compare the price of a mortality bond in four scenarios: no parameter uncertainty, parameter uncertainty with a given prior distribution, parameter uncertainty with Bayesian updates, and parameter uncertainty with the smooth ambiguity preference. We use the indifference pricing approach to derive the minimum ask price and the maximum bid price, and employ the economic pricing method to compute the equilibrium price that clears the market. We reveal the connection between the indifference pricing approach and the economic pricing approach and find that ambiguity aversion has a much smaller effect on prices of mortality-linked securities than risk aversion.